3 problems

Let $A_{\theta}$ be an irrational rotation algebra equipped with the relevant action of a finite cyclic subgroup ${\mathbb{Z}}_n$ of $SL_2({\mathbb{Z}})$, for $n\in\{2,3,4,6\}$. Th…

For an irrational real number $\theta$, let $H_\theta$ denote Harper's operator, obtained from the image of the operator $x+x^{-1}+y+y^{-1}$ in the rotation algebra factor associat…

Rosenberg's conjecture. In this connected component, $E$ attains its minimum exactly at the scalar multiples of $U^mV^n$.